Respuesta :

SaniShahbaz

Answer:

The constant of proportionality is:  

                                                        [tex]k=\frac{1}{2}[/tex]       ∵  k < 1

which is less than 1.

Step-by-step explanation:

  • If [tex]y[/tex] is directly proportional to [tex]x[/tex], then we have

                               [tex]y=kx[/tex]

        where [tex]k[/tex] is said to the the constant of proportionality.

  • If [tex]y[/tex] is inversely proportional to [tex]x[/tex], then we have

                               [tex]y=\frac{k}{x}[/tex]

       where [tex]k[/tex] is said to the the constant of proportionality.

Let us consider the real time example in which the constant of proportionality would be less than one.

The table shows below represents the cups of flour used to make the loaves of bread.

Cups of flour (x)                2          4          8          10

Loaves of bread (y)           1           2          4          5  

As the ratio of x and y is same for all the given values.

i.e.

  • [tex]\frac{2}{1} = 2[/tex]
  • [tex]\frac{4}{2} = 2[/tex]
  • [tex]\frac{8}{4} = 2[/tex]
  • [tex]\frac{10}{5} = 2[/tex]

Therefore, the relationship given in the table will be proportional.

As the value of x is increased when the value of y is increased, so it will be a directly proportional.

So,

         [tex]y=kx[/tex]

        [tex]1=k(2)[/tex]

        [tex]\frac{1}{2} =k[/tex]

        [tex]k=\frac{1}{2}[/tex]

Therefore, the constant of proportionality is:  

                                                        [tex]k=\frac{1}{2}[/tex]       ∵  k < 1

which is less than 1.

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